Ultralocal measure is not canonical

Starting from canonical quantization, we derive the path integral formulation and show that the resulting measure differs from the standard ultralocal one. This difference becomes particularly significant in asymptotically AdS spacetimes, where it leads to a distinct functional space for fluctuations. We will argue that this “canonical” measure helps resolve several conceptual issues, including the choice of admissible boundary conditions and the applicability of supersymmetric localization in such backgrounds.